Chapter 9b: The Special Theory of Relativity

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A "light clock" is an easily understood clock (in terms of the postulates of Special Relativity), but it is important to understand that the effects of relativity that it reveals are just as well exhibited by any clock that measures time, including a Mickey Mouse watch or the beating of your own heart. SURPRISE #3: Observers moving relative to one another (do, do not?) agree on the amount of time their clocks measure and hence the clocks give a relative meaning to time. The discrepancy in measured time is called time and is summarized as "Moving clocks run compared to clocks at rest. It (does, does not?) matter whether the clock is moving towards you or away." We conclude that both observers are exactly right, though they disagree. The "Twin Paradox" is the name given to a particular prediction of Special Relativity, but it is completely understood and is not a paradox at all. The twin paradox is the prediction of Special Relativity that if one of two twins leaves the other, moves at speeds near the speed of light, then turns around and returns, when the two again stand side-by-side, the twin who travelled will be (younger, older?) than the twin who remained behind! The apparent symmetry between the two is broken, because the traveller must turn around. This is a(n) (uniform, accelerated?) motion that is an observable difference between the motions of the two twins. The breaking of the symmetry removes the paradox and Special Relativity make a precise prediction for the difference in the ages. The Haefele-Keating Experiment is a real experiment that has been done by real people and real clocks to test the prediction of Special Relativity about the difference in ages of the two twins of the twin paradox. The result of the experiment (agrees, disagrees?) with the prediction. The muon experiment is a real experiment that has been done by real people and real clocks to test the prediction of Special Relativity about time dilation. The result of the experiment (agrees, disagrees?) with the prediction. SURPRISE #4: "The mass of a moving object increases with increasing speed." This effect is called mass increase and it does not matter whether the object is moving towards you or away. Mass is a measure of the resistance of an object to acceleration. As an object approaches the speed of light, its mass increases to the point that it cannot be accelerated beyond the speed limit set by nature, the speed of light. The increase in mass is not appreciable until one get very close to the speed of light; hence, it was overlooked completely until the 20th century. Mass is still taken as exactly conserved in chemistry. SURPRISE #5: Mass and energy are not separate things, but rather manifestations of the same thing: mass-energy (note the hyphenation). If we exert a force on an object and it moves in the direction of the push, we transfer energy to the object. (This transfer process is called .) If we maintain the force as the object approaches the speed of light, we continue to transfer energy to it, but the speed doesn't increase very much (it can't exceed the speed of light) although its kinetic energy must be increasing because we are transferring energy to it. Kinetic Energy = 1/2 (mass)x(speed)2 We conclude that the energy is taking the form of increasing mass. Thus, energy and mass are manifestation of the same thing! Modern particle accelerators are instruments that are designed to accelerate electrons or protons to high energy and collide them with one another so that, possibly, such things as quarks can be observed in the debris of the collisions. The modern accelerators are real experiments that observe very clearly the mass increase predicted by Special Relativity and none has ever been able to accelerate a particle beyond the speed of light because of it.

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